Brachos 10a mentions a story where Rabbi Meir was being bothered by people and prayed for their demise. His wife Bruria tells him do not pray for them to die, pray that they should repent. He followed his wifes advise and they repented.

Why do we pray in V'Lamalshinim that these people should have no hope (Al Tehi Tsikva), they should be lost (K'Rega Tovaid), they should be cut off quickly (Mehaira Yikoraisu), etc. Why do we not Daven for them to repent?

2 Answers
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Even Shlomo Parshas Ekev discusses this question. He proposes that there is a difference where someone does the sin due to his desires, where then you should pray for him to repent. However when someone someone who is a "Min" with bad thoughts, such a person will not repent and only cause others to sin, and therefore we pray for their demise.

what about the gemara, in Brachos 7, with Rabbi Yehoshua ben Levi, the min (rather than Tzeduki), and the rooster?
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josh waxmanAug 31 '12 at 15:55

I am not sure what you are attempting to point out. If anything it makes my question stronger as we see that Rabbi Yehoshua ben Levi was unable to curse the Tzeduki and Rabbi Yehoshua ben Levi said that he sees that they do not want him to curse this Tzeduki from Shamayim.
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Gershon GoldAug 31 '12 at 16:43

this is an example of a "Min". so according to the conclusion of the gemara, where they don't want a curse for "Minim", how could one pray for their demise. (Tzeduki, by the way, was a late insertion by censors who did not like the term Min, which could include Christians. There weren't Tzedukim in the time of Rabbi Yehoshua ben Levi.)
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josh waxmanAug 31 '12 at 18:26

This does not answer the question. Why did he not introduce this Bracha with a request for them to repent?
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Gershon GoldAug 31 '12 at 15:26

this is the answer of The Rambam, Apokirisin were Jews living the religious life. They concluded that the threat was to great for the Jewish people and asked from god to "stop" them
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danie7L TAug 31 '12 at 15:31

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@danie7LT But God could "stop" them by killing them, or by causing them to repent. Why did Rabban Gamliel pick the former method?
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Double AA♦Aug 31 '12 at 15:45

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rabban gamliel was an earlier generation than r. meir. so he wouldn't have heard bruriah's homiletic interpretation of that pasuk
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josh waxmanAug 31 '12 at 15:58